William Lee and colleagues from the University of Limerick set out to answer a puzzling question about the way bubbles form when different gasses are used to pressurise beer.

Although brewers use carbon dioxide gas to pressurise most beers, they sometimes use a mix of nitrogen and carbon dioxide for dark beers like Guinness.

They do this because nitrogen forms smaller bubbles, giving the drink a creamier head of foam. The trouble is that adding nitrogen also changes the physics of bubble formation.

It turns out that in normal beer, bubble formation starts at so-called nucleation sites around cellulose fibres in the beer and glass. But in stouts pressurised with nitrogen, this doesn't seem to happen.

Simply cracking open a can of nitrogen-pressurised stout and pouring it into a glass doesn't create enough bubbles to form a head. To overcome this, brewers use floating 'widgets' filled with gas that creates millions of bubbles in stout cans.

"If you open a can of stout without letting the widget create any foam, the beer looks completely flat," says Lee.

So he and colleagues in the Mathematics Applications Consortium for Science and Industry set out to discover why.

Nitrogen less soluble than CO2

Adapting a mathematical formula first developed for champagne, they were surprised to find that bubble nucleation does happen when nitrogen is used, but much more slowly.

"Nitrogen is much less soluble than carbon dioxide, which leads to slower diffusion of dissolved nitrogen, in turn leading to slow growth of bubbles," he explains.

To check their theoretical model, the Limerick team did something unusual for mathematicians - an experiment.

"We poured stout over some filter paper from the departmental coffee machine, looked at it under a microscope, and saw bubbles forming in the fibres."

Watching the bubbles form, Lee and colleagues found that a single fibre produced one bubble every 1.28 seconds. Their results appear on the pre-press website arxiv.org and have been accepted for publication in the journal Physical Review E .

At that rate, the group calculated around 4 million cellulose fibres would be needed to produce a good head of beer - equivalent to a 3 centimetre square of coffee filter paper.

Replacing the plastic widget

Lee suggests putting a fibre coating inside the beer can above the line of liquid could therefore serve to create a rich, foamy head of bubbles as the stout is poured, potentially doing away with the need for widgets.

"Widgets are very cheap to manufacture and deploy, but they still add a small cost to the production of a can of stout," he says. "Another problem is removing oxygen from the widgets, which is time consuming. If oxygen from the air is left in the widget it will react with the beer affecting its flavour."

For now, the feasibility of this method is still untested, Lee stresses.

"At this stage in the research I can't say that a fibre coating would definitely reduce these problems, but it is a possibility worth investigating. The global sales of stouts are so huge that even tiny savings could add up to quite significant profits."